When creating a workflow in DNG you create states like New, In Progress, Complete etc.. Each state can optionally be put in a group which have simlar names new, In Progress, Complete etc.
What is the significance of putting the state in a group?

The documenation only says:-

Optional: Select a group that is appropriate for the state. For example, the open group would be appropriate for the Submitted state. If none of the available state groups are appropriate, you can use the Eclipse client to modify an existing state group or to add a state group in the State Groups section of the Workflows page.